Why is the formula for Compton scattering not affected by binding energy?

[LocationX]

Why is it that the formula for compton scattering does not include the binding energy for an electron to the nucleus? Seems like the scattered electron can have a continuous range of energies from 0 to h/mc. Why isn't this quantized?

 

[ansgar]

Why is it that the formula for compton scattering does not include the binding energy for an electron to the nucleus? Seems like the scattered electron can have a continuous range of energies from 0 to h/mc. Why isn't this quantized?

because in the formula one assumes that the electron is free, i.e. binding energy = 0.

 

[jtbell]

Note that with the Compton effect we are using X-ray photons (energy = several 10's of keV) or gamma-ray photons (100's of keV), whereas the original binding energies of the electrons are a few eV. So it's a good approximation to consider the electrons as "free."